Here are some examples of this function written in standard form: y=2x² y=x²+7 y=-x²-3
When creating the graph, it will always make a U-shaped line, which is called a parabola. Here's easy steps to making your graphs on your graphing calculator: 1. Press the y= button. 2. Type in your functions. ex:y=2x² 3. Press the graph button. 4. There's your graph!
Going along with the Parabola is the Minimum, and Maximum point.
Here are the rules:
If in the function a <0, the parabola opens downward and the vertex is a maximum point, or the highest point of the parabola.
If in the function a>0, the parabola opens upward, and the vertex is a minimum point, or the lowest point of the parabola.
10-2 Quadratic Functions
In this lesson we will be symplifying and graphing functions.
There are 4 easy steps to graphing a function:
Step 1- What is the axis of symmetry?
x=-b/2a
y=2x²+4x-3 -(4)/2(2) -4/4= -1 Make a dotted line on your graph at -1.
Step 2- What is the vertex?
Take the axis of symmetry, and plug it into the function.
y=2(-1)²+4(-1)-3 y=2(1)-4-3 y=-5 Make a dot on the axis of symmetry at -5, or point (-1,-5) and on the other side of the axis of symmetry.
Step 3- What is the y-intercept? Plug 0 into the function. y=2(0)²+4(0)-3 y=0+0-3 y=-3 Plot a point on (0,-3) and on the other side of the axis of symmetry which is (-2,-3).
Step 4- One more point! Figure out one more point to plot, picking 1 is easy. y=2(1)²+4(1)-3 y=2(1)+4-3 y=2+1 y=3 Plot one more point on (1,3) and on the other side of the axis of symmetry which is (-3,3).
10-3 Solving Quadratic Equations Solve by square roots
Solve 2x²-98=0 First, add 98 to both sides. 2x²=98 Then divide both sides by 2 to get x² by itself. x²=49 Next find the square roots. √x²=√49 x=7
You can now solve quadratic equations three different ways! By graphing on your calculater, finding the intercepts, and solving by square roots. Here's some review! Lesson Quiz 1
Lesson 10-1 Exploring Quadratic Graphs
Solving by Graphing
Quadratic Function:
y=ax²+bx+c
Here are some examples of this function written in standard form:
y=2x²
y=x²+7
y=-x²-3
When creating the graph, it will always make a U-shaped line, which is called a parabola. Here's easy steps to making your graphs on your graphing calculator:
1. Press the y= button.
2. Type in your functions. ex:y=2x²
3. Press the graph button.
4. There's your graph!
Here's a video if you're having trouble:Quadratic Graph Video
Going along with the Parabola is the Minimum, and Maximum point.
Here are the rules:
If in the function a <0, the parabola opens downward and the vertex is a maximum point, or the highest point of the parabola.
If in the function a>0, the parabola opens upward, and the vertex is a minimum point, or the lowest point of the parabola.
10-2 Quadratic Functions
In this lesson we will be symplifying and graphing functions.
There are 4 easy steps to graphing a function:
Step 1- What is the axis of symmetry?
x=-b/2a
y=2x²+4x-3 -(4)/2(2) -4/4= -1
Make a dotted line on your graph at -1.
Step 2- What is the vertex?
Take the axis of symmetry, and plug it into the function.
y=2(-1)²+4(-1)-3 y=2(1)-4-3 y=-5
Make a dot on the axis of symmetry at -5, or point (-1,-5) and on the other side of the axis of symmetry.
Step 3- What is the y-intercept?
Plug 0 into the function.
y=2(0)²+4(0)-3 y=0+0-3 y=-3
Plot a point on (0,-3) and on the other side of the axis of symmetry which is (-2,-3).
Step 4- One more point!
Figure out one more point to plot, picking 1 is easy.
y=2(1)²+4(1)-3 y=2(1)+4-3 y=2+1 y=3
Plot one more point on (1,3) and on the other side of the axis of symmetry which is (-3,3).
10-3 Solving Quadratic Equations
Solve by square roots
Solve
2x²-98=0
First, add 98 to both sides.
2x²=98
Then divide both sides by 2 to get x² by itself.
x²=49
Next find the square roots.
√x²=√49
x=7
You can now solve quadratic equations three different ways! By graphing on your calculater, finding the intercepts, and solving by square roots. Here's some review!
Lesson Quiz 1
Lesson Quiz 2
Lesson Quiz 3